Decimal sequences for cryptography. A recurring decimal such as 1/7=.142857142857... can be considered a periodic series with the digits 142857 in the base 10. In general, such sequences may be written to any base. The maximum period of such a d-sequence (when the base is not necessarily 10) written for 1/q, q prime, is q-1. A recurring decimal is an expression representing a real number in the decimal numeral system, in which after some point the same sequence of digits repeats infinitely many times. ...

A binary d-sequence may be written as:

a_i = 2ⁱ mod q mod 2

These sequences have been used for error-correction coding, cryptography and as random sequences.

References

• S. Kak and A. Chatterjee, On Decimal Sequences. IEEE Transactions on Information Theory, IT-27: 647 – 652, 1981.
• S. Kak, Encryption and error-correction coding using D sequences. IEEE Transactions on Computers, C-34: 803-809, 1985.

External link

• Watermarking using decimal sequences